No, the Catholic Cathedral is the Cathedral of St Matthew the Apostle -- on M St NW at the eastern edge of Georgetown.
You are thinking of the Basilica of the National Shrine of the Immaculate Conception, located on the campus of CUA. It is the largest Catholic Church in the USA, but Cardinal Wuerl's sede is located at St Matthew's, not the Shrine.
Whatever cathedral it is, I think it’s bizarre to put Darth Vader on it.